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I have tried to understand the concept of pure rolling in rotational dynamics but still some part of the 'proper visualization' of the same is unachievable by me.

For starters, I do understand that pure rolling is when the point of contact does not lose contact with the ground which is okay, the key takeaway from this is that (what I have so far understood) the body is rolling and it stays on the ground that is doesn't bounce up or down while it is in motion

Now, secondly what is the meaning in itself, of rolling like does it mean that the body goes in translational motion whilst undergoing rotational as well ?

Thirdly, is rolling's "antithesis" (of course only seen in practice questions or so) 'sliding' in any manner related to wobbling (I do understand that wobbling means deviation from its mean position and in this case in the positive and negative $z$ axes if we take $xy$ plane)

Lastly what is the 'physical meaning' of $v=r\omega$

Please help me in clarifying the same and if I have assumed wrongly please correct me.

Qmechanic
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SmilebroSmile
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2 Answers2

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I am not sure whether I really understand your question.

$\textit{Pure rolling}$ means rolling (that is rotational and traslational movement) $\textbf{without}$ slipping.

No slipping means that the relative speed of the point of contact of the rolling body w.r.t. the surface on which it rolls is zero.

Furthermore, taken from Wikipedia (https://en.wikipedia.org/wiki/Rolling):

The velocity of any point in the rolling object is given by v = ω × r , where r is the displacement between the particle and the rolling object's contact point (or line) with the surface, and ω is the angular velocity vector. Thus, despite that rolling is different from rotation around a fixed axis, the instantaneous velocity of all particles of the rolling object is the same as if it was rotating around an axis that passes through the point of contact with the same angular velocity.

EigenAle
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Firstly, What is Pure Rolling Motion? In pure rolling motion, a rigid body (typically a wheel or a ball) moves in such a way that it doesn't slip at the point of contact with the ground.

To answer your specific questions:

1. Does Pure Rolling Mean the Object Stays on the Ground?

You’re correct that, in pure rolling, the object stays in contact with the surface—it neither jumps off nor sinks into it. Imagine watching a wheel roll in slow motion: you’d see that the bottommost point (where the wheel touches the ground) keeps changing, but each such point, in that very instant, is stationary relative to the ground. This is what defines pure rolling.

2. Sliding vs. Wobbling: Are They Related?

  • Sliding occurs when there is relative motion between the point of contact and the surface. In sliding, the bottom point of the object has a velocity relative to the ground, meaning it's not momentarily stationary.
  • Wobbling, on the other hand, is a different phenomenon where the center of mass of the rolling object is not following a smooth, predictable path. Wobbling happens due to an imbalance, such as a deformed wheel or uneven mass distribution.

The antithesis of pure rolling is indeed sliding, but wobbling is more related to instability or imbalance rather than slipping.

3. Physical Meaning of $v=r\omega$

$v=r\omega$ gives us a direct relationship between how fast the center of the wheel is moving forward and how fast the wheel is spinning. In essence, $v=r\omega$ ensures that there is no slipping at the point of contact.

Hope this clears your doubts.

Vansh Patel
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